By the time you meet her during the mainline quest, A Path to the Garden, Captain Aelfyr may have done plenty in that makes her worth killing.
If you are unable to stop the Steel Garrote in time, the fanatical group will burn down Fior mes Iverno. As a key figure in the plan, Aelfyr led its execution and took great pleasure in it.
As you will have Giatta will you at this point, she is craving justice for her fallen city herself. On the other hand, Aelfyr makes for a very challenging boss battle depending on your difficulty.
In return for taking the challenge on, however, you will be rewarded with a decent piece of gear from the list of unique armor available in .
If you want to get as much unique gear as possible, you should kill Captain Aelfyr in . Not only did I find this a very satisfactory kill in avenging Fior mes Iverno, but this is also the only way to get her Death Knight Gloves.